# Solutions35

8-2 Hw assignment
Question 1
The amounts (in ounces) of juice in eight randomly selected juice bottles are:
15.1  15.1  15.6  15.9  15.5  15.4  15.9  15.5
Find the margin of error (often denoted as E or EBM) for a 98% confidence interval for the mean amount of juice in all such bottles.
Question 2
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Write the UPPER BOUND for the confidence interval.  Assume that the population has a normal distribution.  Round to the nearest hundredth.

n = 10,  = 11.4, s = 1.4, 95% confidence

Question 3
Let t0 be a specific value of t. Find t0 such that the following statement is true:
P(t ≤ t0) = .005 where df = 20.  Round to the nearest thousandth.
Question 4
Find the value of t0 such that the following statement is true: P(-t0 ≤ t ≤ t0) = .99 where df = 9.  Round to the nearest thousandth.
Question 5
A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 162 milligrams with s = 9 milligrams. Construct a 90% confidence interval for the true mean cholesterol content of all such eggs.  Write the LOWER BOUND for the confidence interval.  Assume that the population has a normal distribution.  Round to the nearest hundredth.
Question 6
Thirty randomly selected students took the calculus final. If the sample mean was 74.2 and the standard deviation was 5.2, find the margin of error (often denoted by E or EBM) of a 99% confidence interval for the mean score of all students.  Round to the nearest hundredth.
Question 7
A random sample of 250 students at a university finds that these students take a mean of 15.8 credit hours per quarter with a standard deviation of 2.3 credit hours. Estimate the mean credit hours taken by a student each quarter using a 90% confidence interval. Round to the nearest hundredth.

Question 8
A sociologist develops a test to measure attitudes towards public transportation, and 37 randomly selected subjects are given the test. Their mean score is 94.6 and their standard deviation is 28.3. Construct the 95% confidence interval for the mean score of all such subjects.  Write the UPPER BOUND for the confidence interval.  Round to the nearest hundredth.
Question 9
The principal randomly selected six students to take an aptitude test.
Their scores were:  53.4  80.3  77.8  57  63.4  73.8
Determine a 90% confidence interval for the mean score for all students.  Write the LOWER BOUND for the confidence interval.  Assume that the aptitude test scores are normally distributed.  Round to the nearest hundredth.
10-3 Hw assignment

Question 3
From the sample statistics, find the value of the pooled estimate of proportion (p¯).  Round to the nearest hundredth.

p¯ = (x1+x2)/(n1+n2)

n1 = 1281  n2 = 1168
x1 = 654  x2 = 865
Question 4
A cola manufacturer invited consumers to take a blind taste test. Consumers were asked to decide which of two sodas they preferred. The manufacturer was also interested in what factors played a role in taste preferences. Below is a printout comparing the taste preferences of men and women.

HYPOTHESIS: PROP. X = PROP. Y

SAMPLES SELECTED FROM soda(brand1,brand2)

males (sex=0, males) (NUMBER = 115)
females (sex=1, females) (NUMBER = 56)

X = males
Y = females

SAMPLE PROPORTION OF X = 0.422018
SAMPLE SIZE OF X = 109
SAMPLE PROPORTION OF Y = 0.25
SAMPLE SIZE OF Y = 52

PROPORTION X – PROPORTION Y = 0.172018
Z = 2.11825

Suppose the manufacturer wanted to test to determine if the males preferred its brand more than the females. Using the test statistic given, compute the appropriate p-value for the test.  Round to the nearest thousandth.

Question 5
A survey asked respondents whether marijuana should be made legal. Calculate a 95% confidence interval for  where pA is the proportion of respondents who answered “legal” in state A and pB is the proportion of respondents who responded “legal” in state B using the information given in the table below.
Write the LOWER BOUND for the confidence interval.  Round to the nearest hundredth.

State A
State B
Legal
771
394
n
1553
1832

Question 9
When blood levels are low at an area hospital, a call goes out to local residents to give blood. The blood center is interested in determining which sex – males or females – is more likely to respond. Random, independent samples of 141 females and 103 males were each asked if they would be willing to give blood when called by a local hospital. A success is defined as a person who responds to the call and donates blood. The goal is to compare the percentage of the successes of the male and female responses. Suppose 54 of the females and 55 of the males responded that they were able to give blood. Find the test statistic that would be used if it is desired to test to determine if a difference exists between the proportion of the females and males who responds to the call to donate blood.  Round to the nearest hundredth.